toms923
toms923,
a MATLAB code which
evaluates the Pfaffian for a dense or banded skew symmetric matrix,
by Michael Wimmer.
Licensing:
The computer code and data files made available on this web page
are distributed under
the MIT license
Languages:
toms923 is available in
a MATLAB version and
a Python version.
Related Data and Programs:
toms923_test
test_matrix,
a MATLAB code which
defines test matrices for which the condition, determinant, eigenvalues,
inverse, null vectors, P*L*U factorization or linear system solution
are already known, including the Vandermonde and Wathen matrix.
Reference:

Michael Wimmer,
Algorithm 923: Efficient Numerical Computation of the Pfaffian for
Dense and Banded SkewSymmetric Matrices,
ACM Transactions on Mathematical Software,
Volume 38, Number 4, Article 30, August 2012.
Source Code:

pfaffian_hessenberg.m,
computes the Pfaffian of a real skewsymmetric matrix.
Based on the real Hessenberg decomposition.

pfaffian_householder.m,
computes the Pfaffian of a skewsymmetric matrix. Based on
the Householder tridiagonalization.

pfaffian_LTL.m,
computes the Pfaffian of a skewsymmetric matrix.
Based on the ParlettReid algorithm.

skew_LTL.m,
computes the LTL^T decomposition of a skewsymmetric matrix
using the ParlettReid algorithm.

skew_tridiagonalize.m,
computes the tridiagonal form of a skewsymmetric matrix under
unitary congruence (Householder tridiagonalization).
Last modified on 12 May 2020.